Mathematics – Operator Algebras
Scientific paper
2007-03-17
Mathematics
Operator Algebras
14 pages, 2 figures
Scientific paper
We show that the quadratic matrix equation $VW + \eta (W)W = I$, for given $V$ with positive real part and given analytic mapping $\eta$ with some positivity preserving properties, has exactly one solution $W$ with positive real part. We point out the relevance of this result in the context of operator-valued free probability theory and for the determination of the asymptotic eigenvalue distribution of band or block random matrices. We also address the problem of a numerical determination of the solution.
Far Reza Rashidi
Helton John William
Speicher Roland
No associations
LandOfFree
Operator-valued semicircular elements: Solving a quadratic matrix equation with positivity constraints does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Operator-valued semicircular elements: Solving a quadratic matrix equation with positivity constraints, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Operator-valued semicircular elements: Solving a quadratic matrix equation with positivity constraints will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-432969